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Approximation Problems in Analysis and Probability
- 1st Edition, Volume 159 - August 18, 2011
- Author: M.P. Heble
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 4 - 5 5 8 2 8 - 2
- eBook ISBN:9 7 8 - 0 - 0 8 - 0 8 7 2 7 0 - 4
This is an exposition of some special results on analytic or C∞-approximation of functions in the strong sense, in finite- and infinite-dimensional spaces. It starts with H. W… Read more
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Request a sales quoteThis is an exposition of some special results on analytic or C∞-approximation of functions in the strong sense, in finite- and infinite-dimensional spaces. It starts with H. Whitney's theorem on strong approximation by analytic functions in finite-dimensional spaces and ends with some recent results by the author on strong C∞-approximation of functions defined in a separable Hilbert space. The volume also contains some special results on approximation of stochastic processes. The results explained in the book have been obtained over a span of nearly five decades.
Weierstrass-Stone Theorem and Generalisations - A Brief Survey. Weierstrass-Stone Theorem. Closure of a Module - The Weighted Approximation Problem. Criteria of Localisability. A Differentiable Variant of the Stone-Weierstrass Theorem. Further Differentiable Variants of the Stone-Weierstrass Theorem. Strong Approximation in Finite-Dimensional Spaces. H. Whitney's Theorem on Analytic Approximation. C∞- Approximation in a Finite-Dimensional Space. Strong Approximation in Infinite-Dimensional Spaces. Kurzweil's Theorems on Analytic Approximation. Smoothness Properties of Norms in Lp-Spaces. C∞-Partitions of Unity in Hilbert Space. Theorem of Bonic and Frampton. Smale's Theorem. Theorem of Eells and McAlpin. Contributions of J. Wells and K. Sundaresan. Theorems of Desolneux-Moulis. Ck-Approximation of Ck by C∞ - A Theorem of Heble. Connection Between Strong Approximation and Earlier Ideas of Bernstein-Nachbin. Strong Approximation - Other Directions. Approximation Problems in Probability. Bernstein's Proof of Weierstrass' Theorem. Some Recent Bernstein-Type Approximation Results. A Theorem of H. Steinhaus. The Wiener Process or Brownian Motion. Jump Processes - A Theorem of Skorokhod. Appendices: 1. Topological Vector Spaces. 2. Differential Calculus in Banach Spaces. 3. Differentiable Banach Manifolds. 4. Probability Theory. Bibliography. Index.
- No. of pages: 244
- Language: English
- Edition: 1
- Volume: 159
- Published: August 18, 2011
- Imprint: North Holland
- Paperback ISBN: 9780444558282
- eBook ISBN: 9780080872704
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